A151119 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, -1), (0, 0, 1), (1, 0, 0), (1, 1, 1)}.

1, 3, 11, 45, 193, 856, 3879, 17876, 83278, 391526, 1853274, 8821865, 42188173, 202532928, 975478800, 4711439386, 22810719846, 110672632168, 537957768862, 2619202481238, 12771020440506, 62352168433666, 304782866427315, 1491399752474199, 7304993671794373, 35812199972052943, 175709497650591825

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A151116 A151117 A151118 * A151120 A151121 A142876

Adjacent sequences: A151116 A151117 A151118 * A151120 A151121 A151122

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved